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Byju's Answer
Standard XII
Mathematics
Existence of Limit
Show that l...
Question
Show that
lim
x
→
0
e
1
/
x
−
1
e
1
/
x
+
1
does not exist.
Open in App
Solution
Given
lim
x
→
0
e
1
x
−
1
e
1
x
+
1
Left hand limit.
L.H.L
=
lim
x
→
0
−
e
1
0
−
−
1
e
1
0
−
+
1
=
e
−
∞
−
1
e
−
∞
+
1
=
0
−
1
0
+
1
=
−
1
we know that
e
∞
=
∞
e
−
∞
=
1
e
∞
=
1
∞
⇒
0
Right hand limit
R.H.L =
lim
x
→
0
+
1
e
0
+
−
1
e
1
0
+
+
1
=
e
∞
−
1
e
∞
+
1
=
e
∞
(
1
−
1
e
∞
)
e
∞
(
1
+
1
e
∞
)
=
1
−
0
1
+
0
=
1
So, here
L
.
H
.
L
≠
R
.
H
.
L
So, limit does not exist.
Suggest Corrections
1
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Q.
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lim
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→
0
e
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/
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−
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+
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